Adaptive tracking of linear systems with arbitrarily time-varying parameters

Single-input single-output linear systems with uncertain (not necessarily slowly) time-varying parameters, subject to unknown bounded additive disturbances, are considered. The output is required to track a given smooth bounded reference trajectory. Under the standard assumptions on the undisturbed system (minimum-phase, known and constant relative degree, known sign of the `high frequency gain´, known upper bound on its order) and without requiring parameters and disturbances to be slowly varying or to have known bounds, the proposed output feedback control assures: (i) boundedness of all closed loop signals; (ii) arbitrarily improved transient performance of the tracking error in terms of L_∞ and L₂ truncated norms with respect to disturbances, parameter estimation errors and parameter time derivatives; (iii) asymptotically vanishing tracking errors when parameters belong to a compact set determined by the controller, parameter time derivatives are L₁∩L_∞ and disturbances are L₂∩L_∞